Unite General Secretary Len McCluskey urged Mr Miliband to say he would govern alone even if the party falls short of a majority in next year’s general election.
The intervention comes amid speculation that David Cameron could try to galvanise the Tory rank-and-file by making the same promise in the run-up to the poll.
In an interview with the BBC’s Newsnight programme, Mr McCluskey said: “Labour, I hope, win the next election outright, but if they are the biggest party then my view is Ed should have the courage of his convictions and govern on a minority government....
“My view is that Ed shouldn’t be sucked into a Lib/Lab pact he should have the courage of his convictions if we are the largest party, he should govern.
“And he should challenge those coalition parties to bring him down if necessary and go back to the people so that there’s a stark alternative.”
Labour and Lib Dem leader Nick Clegg have been seen as positioning for a potential alliance next year.
Ed Balls and Mr Clegg have buried the hatchet after a long-running feud, and the Deputy Prime Minister recently praised the way the Opposition had “changed” under Mr Miliband.
A decision by either main party to rule out a coalition would aim to put the choice for voters into stark relief.
But it would also cause a major strategic headache for the Lib Dems - who are highlighting their ability to temper the excesses of the others as a main selling point.
A senior Lib Dem source said: “The Conservatives will have to write their own manifesto. We’ll see if they end up doing it.
“We heard a lot of predictions from the Conservative Party ahead of the 2010 election about the dangers of a hung parliament. None of those apocalyptic predictions came true.
“The coalition Government has, despite the predictions, provided the country with strong and stable government at a time that it needed it.
“We are not going to get into discussions with Labour or the Conservatives about what happens after the election until the British people have had their say.
“If there is no clear mandate for any party then of course the Liberal Democrats would seek to do our duty to provide a strong, stable government.”